Treebeard's Stumper Answer30 Jan 98

Lots of Pennies

In The New Yorker special Cartoon Issue before Christmas, Warren Miller shows a
butler addressing his wealthy employer: "The fifty-five gallon
drum is completely filled with pennies, sir. Should it be
taken to the bank?"

Warren Miller in The New Yorker, December 15, 1997.

Just how many pennies is that? We won't guess the exact answer of course (or care). But we can
make reasonable estimates in many ways by starting with
what we know and taking it a step further. Submit your
estimates by email, and I'll report the results next week.

How many pennies would fill a 55 gallon drum? Most kids at school counted pennies in a
cup or half-cup and then multiplied x 16 cups/gallon x 55
gallons. The average of our answers was about 300,000
pennies, $3000 worth. I counted a half-cup of pennies
several times and got different answers each time, so
packing and settling are important factors that explain the
spread of our answers. I'm impressed by how close our
estimates were. Pennies weigh 2.6 to 2.7 grams apiece,
so that full drum would weigh about 1800 pounds,
nearly a ton. Better take it to the bank with a truck!

When I counted a half-cup of pennies, I got different answers
every time, varying from 150 to 190 pennies per half-cup.
If a half-cup holds 170 +/- 20 pennies, then 55 gallons holds
299,200 +/- 18,000 pennies. Even two significant digits is pushing it.

I also figured the volume of a penny as:

Volume = 1/4 pi d^2 h = 1/4 pi (3/4) (3/4) (.061) = .027 in^3.

55 gallons is 12,705 in^3, and dividing gives 470,000 pennies total.
That's assuming 100% filling, like melting the pennies and pouring them into the drum.
Then I took 100 ml of pennies and found that it took about
40 ml of water to cover them, for a packing density of about 60%.
This gives a final estimate of 282,000 pennies, in the same neighborhood at least.

Graybear contributes this analysis:

I recently tried a practical test. I filled a 15 ounce
peanut can with water and found its volume to be 20 fluid
ounces, so 352 would fit in the barrel. By adding pennies
one handful at a time, then shaking to compact them before
the next handful, it would hold 916 pennies. By stacking
them, it would hold 1071+. (I didn't actually stack them,
but 21 pennies would lay flat on the bottom, and 51 pennies
could be stacked vertically. Other pennies may have been
able to fit in the interstitial spaces.) Therefore, the
results of the test (322,432 - 376,992+) confirm your
findings.

JUST IN CASE THIS IS A TRICK QUESTION!

If the question were, "How many pennies can you fit in an
empty barrel?", the answer would be 'one, of course, then
the barrel would not be empty'.